📝 SummarXiv

Abstract

Bridging the microscopic and the macroscopic modelling scales in crowd dynamics constitutes an important open challenge for systematic numerical analysis, optimization and control. We propose a combined manifold and machine learning approach to learn the discrete evolution operator for the emergent crowd dynamics in latent spaces from high-fidelity agent-based simulations. The proposed framework builds upon our previous works on next-generation Equation-free algorithms for learning surrogate models of high-dim. multiscale systems. Our approach is a four-stage one, explicitly conserving the mass of the reconstructed dynamics in the high-dim. space. In the first step, we derive continuous macroscopic fields (densities) from discrete microscopic data (pedestrians' positions) using KDE. In the second step, based on manifold learning, we construct a map from the macroscopic ambient space into the latent space parametrized by a few coordinates based on POD of the corresponding density distribution. The third step involves learning reduced-order surrogate ROMs in the latent space using machine learning techniques, particularly LSTMs networks and MVARs. Finally, we reconstruct the crowd dynamics in the high-dim. space in terms of macroscopic density profiles. With this "embed->learn in latent space->lift back to ambient space" pipeline, we create an effective solution operator of the unavailable macroscopic PDE for the density evolution. For our illustrations, we use SFM to generate data in a corridor with an obstacle, imposing periodic boundary conditions. The numerical results demonstrate high accuracy, robustness, and generalizability, thus allowing for fast and accurate modelling of crowd dynamics from agent-based simulations. Notably, linear MVAR models surpass nonlinear LSTMs in predictive accuracy, while also offering significantly lower complexity and greater interpretability.